Fan footage widely shared on social media showed Jones, who had come on as a second-half substitute, gesturing and speaking animatedly with captain Dominik Szoboszlai before the discussion continued with Kostas Tsimikas and Jeremie Frimpong, with Frimpong appearing to step between Jones and his team-mates before eventually leading him away, according to the Daily Mail.
What sparked the exchange has not been confirmed by the club or any player involved, and reports across British outlets have been consistent in stating the cause remains unclear.
The incident came after Andoni Iraola's side made it two wins from two in pre-season, with Rio Ngumoha's deflected second-half strike settling the contest. Jones is widely understood to be a candidate to leave Liverpool this summer, with the club having already turned down a second approach from Inter Milan, reported at around £21.7 million, as too low.
Liverpool are believed to value the academy graduate between £35m and £40m and, with just one year left on his contract, would prefer to let him enter the final year of his deal rather than sell below that valuation. Sources close to the club insist there is no active push to move Jones on despite the gap between the two sides' expectations, though no further contract talks are currently planned.
Jones grew frustrated with a lack of regular starts under former head coach Arne Slot towards the end of last season. By contrast, fellow academy product Trey Nyoni, who made just 21 Premier League minutes all last season, again impressed in New York after catching the eye in Liverpool's previous pre-season fixture against Sunderland.
Jones has been an Anfield regular since coming through Liverpool's academy as a boyhood supporter of the club, and any departure would mark the end of a homegrown career that included Premier League and FA Cup honours.
He was withdrawn from Wednesday's game just after half-time having played around 40 minutes, with Szoboszlai given the captain's armband for the evening in the continued absence of the squad's senior contingent, several of whom have yet to return from their post-World Cup break.